Gigantic diphoton rate of heavy Higgs bosons in the aligned two Higgs doublet models with small tan β

We study the implications of the LHC heavy neutral Higgs boson search data on the aligned two Higgs doublet model with a softly broken Z(2) symmetry. When tan beta is small, the gluon fusion production of the heavy CP-even scalar H-0 or the CP-odd scalar A(0) becomes large enough to constrain the model by the current gamma gamma, tau(+)tau(-), and (tt) over bar data. By reinvestigating the indirect constraints from Delta rho, b -> s gamma, Delta M-Bd, R-b, epsilon(K), and the perturbativity of the running top quark Yukawa coupling, we find that the small tan beta region is still allowed: for instance, tan beta greater than or similar to 0.6(0.5) for Type I and X (II and Y) for m(H)+/- = 800 GeV. We find that the current LHC results of the heavy Higgs searches at root s = 8 TeV are shown to put on more significant bounds. If mH similar or equal to m(A), the (tt) over bar mode excludes tan beta less than or similar to 1.5 for m(H,A) = 500-600 GeV in all four types, and the gamma gamma and tau(+)tau(-) modes exclude tan beta less than or similar to 1-3 (tan beta less than or similar to 3-10) for m(H,A) = 150-340 GeV in Types I, II, and Y (Type X).